Wilcoxon Rank-sum Precedence Test Based On Sorted Set Early Failure Data

In this article,we utilize Wilcoxon's rank-sum statistic into the precedence test based on ranked set sample and prosed three different statistics for testing the equality of two distributions.Three statistics are then proposed based on different assumptions.The exact null distributions of proposed test statistics are derived,critical values are tabulated for set size up to 8 and number of cycles up to 9.The exact power functions of proposed test statistics under the Lehmann alternative:(?)are derived.Then,the power values and their competitors also based on ranked set samples are compared under the Lehmann alternative exactly.In order to further discuss the properties of the three statistics,the power values and their competitors also based on ranked set samples are compared under the location-shift alternative:(?)by Monte Carlo simulations.For the purpose of making the proposed statistics more widely applicable,under the location-shift alternative:(?),we explore the properties of the three statistics in the case of imperfect rankings.We uses an imperfect ranking model with additional noise models,and takes the correlation coefficients ?=0.2,0.4,0.6,0.8.Finally,we can draw the following conclusions:In most cases,the three statistics proposed of us are better than the precedence test statistics based on ranked set samples under the same conditions,and when the original distribution is skewed to the right,it is better than the rank-sum test statistic based on ranked set samples under the same conditions.